Polaron effect on Raman scattering in semiconductor quantum dots

Strong coupling of a confined exciton to optical phonons in semiconductor quantum dots (QDs) leading to the formation of a polaron is considered for a model system including two lowest exciton states and several optical phonon modes. Both intra- and inter-level terms are taken into account. The Hamiltonian has been exactly diagonalized including a finite number of phonons allowed for each mode, large enough to guarantee that the result can be considered exact in the physically important region of energies. Based on this polaron spectrum, the Raman scattering probability is obtained, which is compared with the one calculated using the standard perturbation theory approach. It is shown that, when either diagonal or non-diagonal coupling is sufficiently strong, the Raman spectrum line shape and especially its resonant behaviour differ considerably from the perturbation theory predictions. The dependence of the scattering intensity on the excitation wavelength contains features similar to those expected in the optical absorption spectra of QDs